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Critical densities for Korteweg-de Vries-like acoustic solitons in multi-ion plasmas

Frank Verheest (UGent)
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Organization
Abstract
A generic proof has been given that, for the acoustic mode with the highest velocity in a plasma comprising a number of fluid species and one kind of inertialess electrons, even though there can be critical densities (making the coefficient of the quadratic nonlinearity in a Korteweg-de-Vries equation vanish), no supercritical densities exist (requiring the simultaneous annulment of both the quadratic and cubic nonlinearities in a reductive perturbation treatment). Similar conclusions hold upon expansion of the corresponding Sagdeev pseudopotential treatment. When there is only one (hot) electron species, the highest-velocity mode is an ion-acoustic one, but if there is an additional cool electron species, with its inertia taken into account, the highest-velocity mode is an electron-acoustic mode in a two-temperature plasma. The cool fluid species can have various polytropic pressure–density relations, including adiabatic and/or isothermal variations, whereas the hot inertialess electrons are modelled by extensions of the usual Boltzmann description that include non-thermal effects through Cairns, kappa or Tsallis distributions. Together, in this way quite a number of plasma models are covered. Unfortunately, there seems to be no equivalent generic statement for the slow modes, so that these have to be studied on a case-by-case basis, which for models with more than three species is far from straightforward, given the parameter ranges to be discussed.
Keywords
NEGATIVE-IONS, SOLITARY WAVES, 2-ELECTRON-TEMPERATURE PLASMA, 2-TEMPERATURE ELECTRONS, MATHEMATICAL APPROACH, DUSTY PLASMA, TEMPERATURE, PROPAGATION, STATISTICS

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Citation

Please use this url to cite or link to this publication:

MLA
Verheest, Frank. “Critical Densities for Korteweg-de Vries-like Acoustic Solitons in Multi-ion Plasmas.” JOURNAL OF PLASMA PHYSICS 81.6 (2015): n. pag. Print.
APA
Verheest, F. (2015). Critical densities for Korteweg-de Vries-like acoustic solitons in multi-ion plasmas. JOURNAL OF PLASMA PHYSICS, 81(6).
Chicago author-date
Verheest, Frank. 2015. “Critical Densities for Korteweg-de Vries-like Acoustic Solitons in Multi-ion Plasmas.” Journal of Plasma Physics 81 (6).
Chicago author-date (all authors)
Verheest, Frank. 2015. “Critical Densities for Korteweg-de Vries-like Acoustic Solitons in Multi-ion Plasmas.” Journal of Plasma Physics 81 (6).
Vancouver
1.
Verheest F. Critical densities for Korteweg-de Vries-like acoustic solitons in multi-ion plasmas. JOURNAL OF PLASMA PHYSICS. 2015;81(6).
IEEE
[1]
F. Verheest, “Critical densities for Korteweg-de Vries-like acoustic solitons in multi-ion plasmas,” JOURNAL OF PLASMA PHYSICS, vol. 81, no. 6, 2015.
@article{6991588,
  abstract     = {A generic proof has been given that, for the acoustic mode with the highest velocity in a plasma comprising a number of fluid species and one kind of inertialess electrons, even though there can be critical densities (making the coefficient of the quadratic nonlinearity in a Korteweg-de-Vries equation vanish), no supercritical densities exist (requiring the simultaneous annulment of both the quadratic and cubic nonlinearities in a reductive perturbation treatment). Similar conclusions hold upon expansion of the corresponding Sagdeev pseudopotential treatment. When there is only one (hot) electron species, the highest-velocity mode is an ion-acoustic one, but if there is an additional cool electron species, with its inertia taken into account, the highest-velocity mode is an electron-acoustic mode in a two-temperature plasma. The cool fluid species can have various polytropic pressure–density relations, including adiabatic and/or isothermal variations, whereas the hot inertialess electrons are modelled by extensions of the usual Boltzmann description that include non-thermal effects through Cairns, kappa or Tsallis distributions. Together, in this way quite a number of plasma models are covered. Unfortunately, there seems to be no equivalent generic statement for the slow modes, so that these have to be studied on a case-by-case basis, which for models with more than three species is far from straightforward, given the parameter ranges to be discussed.},
  articleno    = {905810605},
  author       = {Verheest, Frank},
  issn         = {0022-3778},
  journal      = {JOURNAL OF PLASMA PHYSICS},
  keywords     = {NEGATIVE-IONS,SOLITARY WAVES,2-ELECTRON-TEMPERATURE PLASMA,2-TEMPERATURE ELECTRONS,MATHEMATICAL APPROACH,DUSTY PLASMA,TEMPERATURE,PROPAGATION,STATISTICS},
  language     = {eng},
  number       = {6},
  pages        = {10},
  title        = {Critical densities for Korteweg-de Vries-like acoustic solitons in multi-ion plasmas},
  url          = {http://dx.doi.org/10.1017/S0022377815001282},
  volume       = {81},
  year         = {2015},
}

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